Instead of defining a reduced inertia \(\mu\) to characterize the convertible kinetic energy of a system, we could define a reduced velocity \(v_{\text {red }}\) as follows: For a system of two particles, one of inertia \(m_{1}\) and velocity \(v_{1}\) and the other of inertia \(m_{2}\) and velocity \(v_{2}\), the kinetic energy is Derive an expression for the reduced velocity in terms of the given variables. (Just as the center-of-mass velocity is a weighted mean of the individual velocities, the reduced velocity is a weighted difference between the individual velocities.)

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K = Km + Kony (m + my) vm + (m + m) red-